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\begin{document}
\begin{equation}
\begin{aligned}
&\underset{\begin{subarray}{c}
    x(\cdot),\,u(\cdot), \, z(\cdot)
\end{subarray}}{\min}	    &&\int_0^T l(x(\tau), u(\tau), z(\tau), p)\mathrm{d}\tau + m(x(T), z(T), p)\\ 
                            &\,\,\,\quad \text{s.t.}    &&x(0) - \bar{x}_0 = 0, &&\\
                            & 						    &&\underline{x}_0 \leq \Pi_{x_0}x(0) \leq \bar{x}_0, && \\
                            & 						    &&\underline{u}_0 \leq \Pi_{u_0}u(0) \leq \bar{u}_0, && \\
                            & 						    &&\underline{z}_0 \leq \Pi_{z_0}z(0) \leq \bar{z}_0, && \\
                            & 						    &&\underline{c}_0 \leq C_0x(0) + D_0u(0) + E_0z(0)\leq \bar{c}_0, && \\
                            &                           &&                                                   && \\[-1em]  
                            & 						    &&F(x(t), \dot{x}(t), u(t), z(t), p) = 0, &&\quad t \in [0,\,T),\\
                            & 						    &&\underline{h} \leq g(h(x(t), u(t), z(t), p)) \leq \bar{h}, &&\quad t \in [0,\,T),\\
                            & 						    &&\underline{x} \leq \Pi_{x}x(t) \leq \bar{x}, &&\quad t \in (0,\,T),\\
                            & 						    &&\underline{u} \leq \Pi_{u}u(t) \leq \bar{u}, &&\quad t \in (0,\,T),\\
                            & 						    &&\underline{z} \leq \Pi_{z}z(t) \leq \bar{z}, && \quad t \in (0,\,T),\\
                            & 						    &&\underline{c} \leq Cx(t) + Du(t) + Ez(t)\leq \bar{c}, &&\quad t \in (0,\,T), \\
                            &                           &&                                                   && \\[-1em] 
                            & 						    &&F_T(x(T), z(T), p) = 0, &&\\
                            & 						    &&\underline{h}_T \leq g_T(h_T(x(T), z(T), p)) \leq \bar{h}_T, &&\\
                            & 						    &&\underline{x}_T \leq \Pi_{x_T}x(T) \leq \bar{u}_{T}, &&\\
                            & 						    &&\underline{z}_T \leq \Pi_{z_T}z(T) \leq \bar{z}_T, && \\
                            & 						    &&\underline{c}_T \leq C_Tx(T) + E_Tz(T)\leq \bar{c}_T, &&\\
\end{aligned}
\end{equation}
where $l\vcentcolon \mathbb{R}^{n_x}\times\mathbb{R}^{n_u}\times\mathbb{R}^{n_z} \rightarrow \mathbb{R}$, $m\vcentcolon \mathbb{R}^{n_x}\times\mathbb{R}^{n_z} \rightarrow \mathbb{R}$ are the Lagrange and Mayer objective terms, respectively. The function $F\vcentcolon \mathbb{R}^{n_x}\times\mathbb{R}^{n_x}\times\mathbb{R}^{n_u}\times\mathbb{R}^{n_z}\times\mathbb{R}^{n_p} \rightarrow \mathbb{R}^{n_x+n_z}$, represents the (potentially) fully implicit dynamics
of the system, while $F_T\vcentcolon \mathbb{R}^{n_x}\times\mathbb{R}^{n_z}\times\mathbb{R}^{n_p} \rightarrow \mathbb{R}^{n_x+n_z}$ describes the terminal algebraic constraint. The constraints are described by the general nonlinear functions, $h\vcentcolon \mathbb{R}^{n_x}\times\mathbb{R}^{n_u}\times\mathbb{R}^{n_z}\times\mathbb{R}^{n_p} \rightarrow \mathbb{R}^{n_h}$ and $h_T\vcentcolon \mathbb{R}^{n_x}\times\mathbb{R}^{n_z}\times\mathbb{R}^{n_p} \rightarrow \mathbb{R}^{n_{h_T}}$ and the nonlinear convex functions $g\vcentcolon \mathbb{R}^{n_h} \rightarrow \mathbb{R}^{n_g}$ and $g_T\vcentcolon \mathbb{R}^{n_{h_T}} \rightarrow \mathbb{R}^{n_{g_T}}$. 
\par
\vspace{0.2cm}
Currently not yet implemented features:
\begin{itemize}
    \item $l$ must be in linear least-squares form $l = \frac{1}{2}\| V_x x(t) + V_u u(t) + V_z z(t)\|_W^2$ 
    \item support for soft constraints missing 
    \item constraints cannot depend on algebraic variables (yet)

\end{itemize}
\end{document}

